Geometry & Topology

Strand algebras and contact categories

Daniel V Mathews

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Abstract

We demonstrate an isomorphism between the homology of the strand algebra of bordered Floer homology, and the category algebra of the contact category introduced by Honda. This isomorphism provides a direct correspondence between various notions of Floer homology and arc diagrams, on the one hand, and contact geometry and topology on the other. In particular, arc diagrams correspond to quadrangulated surfaces, idempotents correspond to certain basic dividing sets, strand diagrams correspond to contact structures, and multiplication of strand diagrams corresponds to stacking of contact structures. The contact structures considered are cubulated, and the cubes are shown to behave equivalently to local fragments of strand diagrams.

Article information

Source
Geom. Topol., Volume 23, Number 2 (2019), 637-683.

Dates
Received: 12 February 2017
Revised: 19 March 2018
Accepted: 28 June 2018
First available in Project Euclid: 17 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.gt/1555466428

Digital Object Identifier
doi:10.2140/gt.2019.23.637

Mathematical Reviews number (MathSciNet)
MR3939043

Zentralblatt MATH identifier
07056051

Subjects
Primary: 53D10: Contact manifolds, general 57R17: Symplectic and contact topology 57R58: Floer homology
Secondary: 18F99: None of the above, but in this section

Keywords
strand algebra contact category contact structures bordered Floer homology

Citation

Mathews, Daniel V. Strand algebras and contact categories. Geom. Topol. 23 (2019), no. 2, 637--683. doi:10.2140/gt.2019.23.637. https://projecteuclid.org/euclid.gt/1555466428


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